Referring to copending U.S. application Ser. No. 623,438, when a fundamental frequency of a periodically varying signal is substantially determined and is varied in time or in space, it is required in various measuring fields that the fundamental frequency be exactly estimated every moment or in each location within the space utilizing an interference fringe. Such a periodic signal is a continuous analog signal originally, but in order to perform the signal processing exactly at high speed, the signal is read discretely at definite sampling points and is digitized and processed. Calculation of the above-mentioned fundamental frequency is also performed in such discrete reading and digitizing, and fast Fourier transformation (FFT) is widely used in this case. When the periodically varying signal is read at regular intervals of sampling points and the data are used as an input and complex fast Fourier transformation is performed, if the input signal is plus or positive, for example, and is composed of a fundamental frequency which is substantially constant, data as FFT results obtained discretely have the maximum of the absolute values on positions corresponding to the fundamental frequency. Since the results of FFT are discrete, in order to estimate the fundamental frequency exactly, estimation of the sampling points providing the maximum value appearing only in the neighborhood of the fundamental value is quite insufficient. Therefore, in copending U.S. application Ser. No. 623,438, data in the sampling point j.sub.0 to provide the maximum value and both sampling points j.sub. 0 -1, j.sub.0 +1 adjacent to j.sub.0, that is, three pieces of data in total, are used, and interpolation application close to secondary approximation is performed and the interpolation spectral peak position J.sub.0 +.DELTA.' (.vertline..DELTA.'.vertline..ltoreq.0.5) is estimated.
In the aforedescribed method, when the fundamental frequency exists in the neighborhood of the sampling points, the fundamental frequency can be estimated exactly, by the secondary approximation of data at the three sampling points, J.sub.0 -1, j.sub.0, j.sub.0 +1, but when the fundamental frequency comes near an intermediate point between the two neighboring sampling points, significant error is produced. The greater the noise component of low frequency or high frequency other than the fundamental frequency component, the greater the error. Consequently, it becomes difficult to estimate the measured value from the fundamental frequency exactly.